Big one

July 06, 2010 7:01 AM
by

Longshot sometimes is best play

When my father, Lenny Frome, started to analyze video poker more than two decades ago, I think one of the most startling revelations he made was how to play a hand with a smattering of high cards. We were never all that sure how the manufacturers first calculate the payback of video poker. We long surmised that they basically ‘assumed’ how certain hands should be played without looking at it from a 100% math perspective. These hands tend to bolster the case for this.

If you were playing 5-card draw poker at home with your buddies and you were dealt the following:

There is a pretty good chance that what you will hold is the J-Q-A. You figure you have some long odds for the straight, but always possible and you’ll have two chances to pick up a High Pair, including a Pair of Aces. While it might be nice to wind up with a Flush instead of a Straight or a Straight Flush even, when playing against your friends, an Ace High Straight is probably just as unbeatable as a Flush or the Straight Flush. You are VERY likely to win.

Video Poker doesn’t work anything like this. Each winning hand has a payout all its own. So, in full-pay jacks or better, a Straight pays 4 and a Flush pays 6. The Straight Flush pays 50 and the Royal Flush pays a whopping 800 (with max-coin in). Thus, there are a lot of reasons to go for a Royal Flush when playing video poker relative to poker. This brings me back to what my father discovered.

When dealt a hand like the one above in video poker, the payout of the Straight Flush and Royal Flush compels us to discard the Ace. Holding the Ace increases our chances of pulling the Straight or a High Pair. In fact, we have a nearly 40% higher chance of getting that Straight. We have about 6% greater chance of getting a High Pair by holding the three High Cards.

Discarding the Ace on the other hand opens up a world of possibilities. First of all, we now have a chance to draw a Flush. We also double our chances of getting Three of a Kind. While they are longshots, we also create possibilities to draw Four of a Kinds, Straight Flushes or even the Royal Flush.

There are 16,215 possible draws when drawing 3 cards … 5 of them will result in one of these three possible hands. Thus, it is a 3200+ to 1 shot, but these hands will pay 950 units when all are hit. As such, they add a great deal to the calculation of our expected value.

In fact, when we look at the entire picture, the win frequency is actually a bit greater by holding just the two suited cards. Even if the J-Q were NOT suited (and didn’t match the Ace), the right play would be to hold just these two.

As I’ve discussed in prior columns, an Ace in video poker is not as valuable as an Ace in regular poker. By holding the Ace, you greatly reduce your chances of drawing a Straight because you make the Straight into an Inside (or Double Inside) Straight. So, what you gain by holding a 3rd card in the sequence is mostly given back by the fact that what you are holding is an Ace.

This is why in certain circumstances we DO hold an off-suit King with a J-Q (if all 3 are of different suits). In this case, we are not giving up any chances for a Flush (none of the cards are suited) and because it is a King, the probability of drawing the Straight goes up by enough to offset what we are giving up.

To recap, we hold TWO suited High Cards over THREE unsuited High Cards. We NEVER hold an Ace as part of Three High Cards (unless a 3-Card Royal!). We only hold three High Cards when it is a J-Q-K, all unsuited.